Extension of CR mappings between generic algebraic submanifolds

Slobodan M. Kojcinovic

Vol. 220 (2005), No. 2, 359–378

DOI: 10.2140/pjm.2005.220.359

Abstract

We prove a holomorphic extension theorem for CR mappings between real algebraic submanifolds of ℂ^N. The source and the target manifolds are assumed to be generic submanifolds of equal dimension with source being connected, holomorphically nondegenerate, and having at least one point at which it is of finite type. The mapping H is assumed to be a smooth mapping which is a local diffeomorphism near at least one point of the source. In proving our main result, we construct a CR function which is nonzero at a given point of the source if and only if H is a local diffeomorphism near that same point.

Keywords

CR submanifold, CR mapping, holomorphic extension, algebraic submanifold

Mathematical Subject Classification 2000

Primary: 32H02

Milestones

Received: 4 August 2000

Accepted: 15 October 2001

Published: 1 June 2005